Graduate Certificate Programs

Graduate Certificate ProgramsThe Department currently offers graduate certificates in Applied Statistics and Stochastic Systems. Each program consists of four courses, including one elective chosen with the consent of the departmental advisor. Most courses may be used toward a master's degree, as well as for the certificate. The required courses and list of approved electives are included below. Admission requirements are the same as for the master's programs.

An introduction to the applied nonlinear regression, multiple regression and time-series methods for modeling civil and environmental engineering processes. Topics include: coefficient estimation of linear and nonlinear models; construction of multivariate transfer function models; modeling of linear and nonlinear systems; forecast and prediction using multiple regression and time series models; statistical quality control techniques; ANOVA tables and analysis of model residuals. Applications include monitoring and control of wastewater treatment plants, hydrologic-climatic histories of watercourses, and curve-fitting of experimental and field data.

This course starts with the design and analysis of one factor analysis of variance. Methods of testing specific questions using planned comparisons are stressed. Models with two or more factors are considered with detailed instruction on the analysis of interactions. Repeated-measures designs are also covered, as well as designs with random and fixed factors.

The objective of this course is to introduce the students to the basic results of convex analysis and optimization. The properties of nonlinear non-smooth optimization models will be analyzed. Topics include: separation and representation of convex sets, properties of convex functions, subgradients, optimality conditions, saddle points, constraint qualifications, Fenchel and Lagrange duality, and sensitivity analysis. Examples of optimization models from probability, statistics, and approximation theory will be discussed, as well as some basic models from management, finance, telecommunications, and other fields.

The objective of this course is to introduce the students to the most popular numerical methods for solving nonlinear and non-smooth optimization problems. The techniques will be based on the properties of nonlinear non-smooth optimization models and optimality conditions. Linear optimization techniques will be treated as a special case. Some emphasis will be put on using optimization software. Examples using AMPL and CPLEX will be demonstrated in class. Topics include line search, non-derivative methods, basic decent methods, conjugate gradient methods, subgradient methods, Newton methods, projection methods, penalty, barrier, interior point methods, Lagrangian methods, bundle methods, trust-region method, numerical treatment of non-convex models, and decomposition methods.

The main purpose of this course is to present the foundations of the stochastic control theory, the corresponding numerical methods, and some applications. The focus will be on the idea of dynamic programming which will be developed starting from deterministic models, through finite-horizon stochastic problems, to infinite-horizon stochastic problems of various types. Applications to queuing systems, network design, and routing; supply-chain management and others will be discussed in detail. Topics to be covered: basic concepts of control theory for stochastic dynamic systems; controlled Markov chains; dynamic programming for finite horizon problems; infinite horizon discounted problems; numerical methods for infinite horizon problems; linear stochastic dynamic systems in discrete time; tracking and Kalman filtering; linear quadratic models; controlled Markov processes in continuous time; and elements of stochastic control theory in continuous time and state space.